chew the cud upon sth;rack (/beat/crack/cudgel/ransack) one’s brains;think one’s head off; work one’s head to the bone
❍ 他在～考虑一条妥善的道路，使自己安全的出去，又安全的回来。(梁斌《红旗谱》) 422) He racked his brains for a safe way by which to slip out and return。
绞尽脑汁jiǎo jìn nǎo zhī
绞：挤压。比喻费尽心机，想尽办法。rack one’s brains, puzzle one’s brains out, beat one’s brains, cudgel one’s brains, drag one’s brains